Application Of Neural Network To Constrained Optimization Problems Using Penalty Function Approach

ABSTRACT

In this research work we propose a feed forward neural network for solving constrained optimization problems with inequality and equality constraints. We employ penalty functions that transformed a constrained problem into a single unconstrained problem. The constraints are placed into the objective function via a penalty parameter in such a way that penalizes any violation of the constraints. The penalty function constructed is actually an energy function for the neural network. Assuming differentiability, a local minimum of the penalty function is found by using a dynamic gradient scheme which provides a system of differential equations for the input neurons corresponding to the variables of the given optimization problem. These can then be solved to give solutions which converge ultimately to the optimal solution of the constrained optimization problem. We discovered that our approach is easier and fast and reduces the vigorous steps and assumptions in other methods. Mathcad 14 was used in executing the program.`